The Distribution of Totally Positive Integers in Totally Real Number Fields

Hecke studies the distribution of fractional parts of quadratic irrationals with Fourier expansion of Dirichlet series. This method is generalized by Behnke and Ash-Friedberg, to study the distribution of the number of totally positive integers of given trace in a general totally real number field of any degree. When the number field is quadratic, Beck also proved a mean value result using the continued fraction expansions of quadratic irrationals. We generalize Beck’s result to higher moments. When the field is cubic, we show that the asymptotic behavior of a weighted Diophantine sum is related to the structure of the unit group. The main term can be expressed in terms of Grossencharacter L -functions

Inputs to the Dorsal Striatum of the Mouse Reflect the Parallel Circuit Architecture of the Forebrain

The basal ganglia play a critical role in the regulation of voluntary action in vertebrates. Our understanding of the function of the basal ganglia relies heavily upon anatomical information, but continued progress will require an understanding of the specific functional roles played by diverse cell types and their connectivity. An increasing number of mouse lines allow extensive identification, characterization, and manipulation of specified cell types in the basal ganglia. Despite the promise of genetically modified mice for elucidating the functional roles of diverse cell types, there is relatively little anatomical data obtained directly in the mouse. Here we have characterized the retrograde labeling obtained from a series of tracer injections throughout the dorsal striatum of adult mice. We found systematic variations in input along both the medial–lateral and anterior–posterior neuraxes in close agreement with canonical features of basal ganglia anatomy in the rat. In addition to the canonical features we have provided experimental support for the importance of non-canonical inputs to the striatum from the raphe nuclei and the amygdala. To look for organization at a finer scale we have analyzed the correlation structure of labeling intensity across our entire dataset. Using this analysis we found substantial local heterogeneity within the large-scale order. From this analysis we conclude that individual striatal sites receive varied combinations of cortical and thalamic input from multiple functional areas, consistent with some earlier studies in the rat that have suggested the presence of a combinatorial map

A Role for Myosin VI in the Localization of Axonal Proteins

In neurons polarized trafficking of vesicle-bound membrane proteins gives rise to the distinct molecular composition and functional properties of axons and dendrites. Despite their central role in shaping neuronal form and function, surprisingly little is known about the molecular processes that mediate polarized targeting of neuronal proteins. Recently, the plus-end-directed motor Myosin Va was shown to play a critical role in targeting of transmembrane proteins to dendrites; however, the role of myosin motors in axonal targeting is unknown. Here we show that Myosin VI, a minus-end-directed motor, plays a vital role in the enrichment of proteins on the surface of axons. Engineering non-neuronal proteins to interact with Myosin VI causes them to become highly concentrated at the axonal surface in dissociated rat cortical neurons. Furthermore, disruption of either Myosin VI function or expression leads to aberrant dendritic localization of axonal proteins. Myosin VI mediates the enrichment of proteins on the axonal surface at least in part by stimulating dendrite-specific endocytosis, a mechanism that has been shown to underlie the localization of many axonal proteins. In addition, a version of Channelrhodopsin 2 that was engineered to bind to Myosin VI is concentrated at the surface of the axon of cortical neurons in mice in vivo, suggesting that it could be a useful tool for probing circuit structure and function. Together, our results indicate that myosins help shape the polarized distributions of both axonal and dendritic proteins

Singular moduli for a distinguished non-holomorphic modular function

Here we study the integrality properties of singular moduli of a special non-holomorphic function γ(z) which was previously studied by Siegel [10], Masser [8], Bruinier, Sutherland, and Ono [3]. Similar to the modular j-invariant, γ has algebraic values at any CM-point. We show that primes dividing the denominators of these values must have absolute value less than that of the discriminant and are not split in the corresponding quadratic field. Moreover we give a bound for the size of the denominator

Integrating Stock Features and Global Information via Large Language Models for Enhanced Stock Return Prediction

The remarkable achievements and rapid advancements of Large Language Models (LLMs) such as ChatGPT and GPT-4 have showcased their immense potential in quantitative investment. Traders can effectively leverage these LLMs to analyze financial news and predict stock returns accurately. However, integrating LLMs into existing quantitative models presents two primary challenges: the insufficient utilization of semantic information embedded within LLMs and the difficulties in aligning the latent information within LLMs with pre-existing quantitative stock features. We propose a novel framework consisting of two components to surmount these challenges. The first component, the Local-Global (LG) model, introduces three distinct strategies for modeling global information. These approaches are grounded respectively on stock features, the capabilities of LLMs, and a hybrid method combining the two paradigms. The second component, Self-Correlated Reinforcement Learning (SCRL), focuses on aligning the embeddings of financial news generated by LLMs with stock features within the same semantic space. By implementing our framework, we have demonstrated superior performance in Rank Information Coefficient and returns, particularly compared to models relying only on stock features in the China A-share market.Comment: 8 pages, International Joint Conferences on Artificial Intelligenc

Identification, expression, and phylogenetic analyses of terpenoid biosynthesis-related genes in secondary xylem of loblolly pine (Pinus taeda L.) based on transcriptome analyses

Loblolly pine (Pinus taeda L.) is one of the most important species for oleoresin (a mixture of terpenoids) in South China. The high oleoresin content of loblolly pine is associated with resistance to bark beetles and other economic benefits. In this study, we conducted transcriptome analyses of loblolly pine secondary xylem to gain insight into the genes involved in terpenoid biosynthesis. A total of 372 unigenes were identified as being critical for oleoresin production, including genes for ATP-binding cassette (ABC) transporters, the cytochrome P450 (CYP) protein family, and terpenoid backbone biosynthesis enzymes. Six key genes involved in terpenoid biosynthetic pathways were selected for multiple sequence alignment, conserved motif prediction, and phylogenetic and expression profile analyses. The protein sequences of all six genes exhibited a higher degree of sequence conservation, and upstream genes were relatively more conserved than downstream genes in terpenoid biosynthetic pathways. The N-terminal regions of these sequences were less conserved than the C-terminal ends, as the N-terminals were quite diverse in both length and composition. The phylogenetic analyses revealed that most genes originated from gene duplication after species divergence, and partial genes exhibited incomplete lineage sorting. In addition, the expression profile analyses showed that all six genes exhibited high expression levels during the high-oleoresin-yielding phase

Isolation and Characterization of Few-layer Manganese Thiophosphite

This work reports an experimental study on an antiferromagnetic honeycomb lattice of MnPS$_3$ that couples the valley degree of freedom to a macroscopic antiferromagnetic order. The crystal structure of MnPS$_3$ is identified by high resolution scanning transmission electron microscopy. Layer dependent angle resolved polarized Raman fingerprints of the MnPS$_3$ crystal are obtained and the Raman peak at 383 cm$^{-1}$ exhibits 100% polarity. Temperature dependences of anisotropic magnetic susceptibility of MnPS$_3$ crystal are measured in superconducting quantum interference device. Magnetic parameters like effective magnetic moment, and exchange interaction are extracted from the mean field approximation mode. Ambipolar electronic transport channels in MnPS$_3$ are realized by the liquid gating technique. The conducting channel of MnPS$_3$ offers a unique platform for exploring the spin/valleytronics and magnetic orders in 2D limitation.Comment: 16 pages, 6 figure